S E C T I O N 5 . 5

SOLVING MULTI-STEP EQUATIONS AND

INEQUALITIES

OBJECTIVES

• Solve multi-step equations

• Solve multi-step inequalities

NOTES

• You can solve equations and inequalities with grouping symbols.

• First, use the Distributive Property to remove the grouping symbols.

EXAMPLES

• 1. 3 = 4(x + 2)

• 2. 4(b - 3) < 72

EXAMPLES

• 3. Solve 4(x + 5) = 3(2x + 4)

• 4. 12m + 12 = 6(3m + 3)

WORD PROBLEM

• Mariella’s parents have budgeted $575 for her birthday party. The cost of the party room is $75. How much can the family spend per guest on food if each of the 40 guests receives a $5 favor? Write and solve an equation.

SOLVE MULTI-STEP INEQUALITIES

• Solve each inequality. Graph the solution on a number line.

• 5. -2(k + 1) > -16+ 5k

• 6. 2p + 5 > 3(p - 6)

NO SOLUTION OR ALL NUMBERS AS SOLUTIONS

• Some equations have no solution. When this occurs, the solution is the __________________, shown by the symbol 0 or ().

• Other equations may have every number as their solution.

• An equation that is true for every value of the variable is called an __________.

EXAMPLES

• 1. 3(y - 5) + 25 = 3y + 10

• 2. -5s – 14 = 2(2s + 3) – 9s

EXAMPLES

• 3. -2(3r + 4) = -5r – 8 – r

• 4. 14 + 8w = 4(8 + 2w)

H.O.T. PROBLEMS

• 1. Write a multi-step inequality that can be solved by first adding 3 to each side.

• 2. Explain how you can solve45> -6x + 3 without multiplying or dividing by a negative number.